6.NS.5: Positive and Negative Numbers in Context
Also written as 6.NS.C.5 and CCSS.MATH.CONTENT.6.NS.C.5 · Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.
The Official Wording
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026
What 6.NS.5 Means in Plain English
Sixth graders meet negative numbers through situations with two opposite directions: 8 degrees below zero is -8, a $20 withdrawal is -20, a submarine 150 feet below the surface is at -150 feet. For each one they say what 0 stands for: freezing, no money moving, sea level.
No arithmetic with negatives yet, just reading, writing and explaining them. The number line placement comes next in 6.NS.6, ordering and absolute value in 6.NS.7, and adding and subtracting signed numbers waits for 7th grade (7.NS.1), where a $20 withdrawal and a $20 deposit cancel to 0.
6.NS.5 I Can Statements
- I can write a real-world quantity as a positive or negative number.
- I can explain what 0 means in a situation.
- I can name the opposite of a quantity, like -8 for 8.
6.NS.5 Worked Example
A weather report and a bank statement, read the same way: decide what 0 means, then decide which direction is positive.
At 6 a.m. the temperature was 12 °C below zero, and by noon it was 15 °C above zero. Jamal’s bank statement shows a deposit of $45 and a withdrawal of $60. Write each quantity as a signed number and say what 0 means in each case.
- Temperature first. On the Celsius scale 0 is freezing, so above zero is positive and below zero is negative.6 a.m.: -12 °C, noon: 15 °C
- Read both numbers as positions on a thermometer: 12 degrees on the cold side of freezing, then 15 degrees on the warm side.-12 is 12 below 0, 15 is 15 above 0
- Money next. Here 0 means the balance did not change. Money in is positive, money out is negative.deposit: +45, withdrawal: -60
- Each number has an opposite of the same size in the other direction. The sign carries the direction, so it is never optional.The opposite of -12 is 12, the opposite of 45 is -45
Check it: Read each number back as a sentence: -60 means 60 dollars left the account. If the sentence sounds wrong, the sign is wrong.
Common Mistakes with 6.NS.5
Dropping the sign because the context already says it
“A withdrawal of $60” recorded as 60
Try this: Ask which direction the number points. Withdrawals take money out, so the record must show -60, or the balance math fails later.
Treating 0 as “nothing”
“0 °C means there is no temperature”
Try this: Name what 0 stands for in every situation: freezing point, sea level, no change. It is a reference point, not an absence.
Reading the minus sign as subtraction
“-150 feet” read as “minus 150”, then asking what to subtract it from
Try this: Read the sign as a direction word: “negative 150” or “150 below sea level”. Subtraction with negatives comes in 7th grade.
Where 6.NS.5 Fits
Practice 6.NS.5
Quick Check
- A diver is 35 feet below the surface. Write her depth as a signed number and say what 0 means.
- What is the opposite of -14? If -14 means 14 degrees below zero, what does the opposite mean?
- A football team gains 8 yards on one play and loses 3 on the next. Write both plays as signed numbers.